A cylindrical vessel of diameter `0.3 m` and height `0.6 m` is filled two thirds with a liquid of specific gravity `0.8`. The vessel is rotated about its axis. a. Determine the speed of rotation when the liquid just starts spilling. b.Find the speed of rotation when the base is just visible. c. What is the percentate of liquid left in the vessel?

Explanation

To solve the problem step by step, we will break it down into parts (a), (b), and (c).

### Given Data:
- Diameter of the cylindrical vessel, \( D = 0.3 \, \text{m} \)
- Radius of the vessel, \( r = \frac{D}{2} = \frac{0.3}{2} = 0.15 \, \text{m} \)
- Height of the vessel, \( h = 0.6 \, \text{m} \)
- Height of liquid in the vessel, \( h_{liquid} = \frac{2}{3} \times h = \frac{2}{3} \times 0.6 = 0.4 \, \text{m} \)
- Specific gravity of the liquid, \( SG = 0.8 \)
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